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|---|---|---|---|
| 1 | // | ||
| 2 | // ====================================================================== | ||
| 3 | // \title RedBlackTreeSetOrMapImpl | ||
| 4 | // \author bocchino | ||
| 5 | // \brief An implementation of a set or map based on a red-black tree | ||
| 6 | // ====================================================================== | ||
| 7 | |||
| 8 | #ifndef Fw_RedBlackTreeSetOrMapImpl_HPP | ||
| 9 | #define Fw_RedBlackTreeSetOrMapImpl_HPP | ||
| 10 | |||
| 11 | #include <limits> | ||
| 12 | |||
| 13 | #include "Fw/DataStructures/ExternalArray.hpp" | ||
| 14 | #include "Fw/DataStructures/ExternalStack.hpp" | ||
| 15 | #include "Fw/DataStructures/SetOrMapImplConstIterator.hpp" | ||
| 16 | #include "Fw/DataStructures/SetOrMapImplEntry.hpp" | ||
| 17 | #include "Fw/Types/Assert.hpp" | ||
| 18 | #include "Fw/Types/SuccessEnumAc.hpp" | ||
| 19 | |||
| 20 | namespace Fw { | ||
| 21 | |||
| 22 | //! This class template implements a red-black tree that can be used as a | ||
| 23 | //! set or map. A red-black tree is a binary search tree (BST) such that | ||
| 24 | //! each node is colored red or black. A red-black tree is valid if | ||
| 25 | //! | ||
| 26 | //! 1. It satisfies the red child invariant: No red node has a red child. | ||
| 27 | //! | ||
| 28 | //! 2. It satisfies the black height invariant (described below). | ||
| 29 | //! | ||
| 30 | //! The black height invariant of a red-black tree T is checked with respect to the | ||
| 31 | //! leaf-augmented tree T'. T' is constructed from T by replacing every "missing" | ||
| 32 | //! node in T (i.e., every place where there could be a child but is not) with | ||
| 33 | //! a new black node. The black height invariant says that for every node N in T', | ||
| 34 | //! every path from N to a leaf in T' goes through the same number of black nodes. | ||
| 35 | //! | ||
| 36 | //! A valid red-black tree is balanced, in the sense that the find operation | ||
| 37 | //! takes O(log n) steps. | ||
| 38 | template <typename KE, typename VN> | ||
| 39 | class RedBlackTreeSetOrMapImpl final { | ||
| 40 | // ---------------------------------------------------------------------- | ||
| 41 | // Friend class for testing | ||
| 42 | // ---------------------------------------------------------------------- | ||
| 43 | |||
| 44 | template <typename KK, typename VV> | ||
| 45 | friend class RedBlackTreeSetOrMapImplTester; | ||
| 46 | |||
| 47 | public: | ||
| 48 | // ---------------------------------------------------------------------- | ||
| 49 | // The Node type | ||
| 50 | // ---------------------------------------------------------------------- | ||
| 51 | |||
| 52 | //! Node | ||
| 53 | class Node { | ||
| 54 | public: | ||
| 55 | //! Color | ||
| 56 | enum class Color : U8 { BLACK, RED }; | ||
| 57 | |||
| 58 | //! Direction | ||
| 59 | enum class Direction : U8 { LEFT, RIGHT }; | ||
| 60 | |||
| 61 | //! The type of a node index | ||
| 62 | using Index = FwSizeType; | ||
| 63 | |||
| 64 | //! The type of an entry in the set or map | ||
| 65 | using Entry = SetOrMapImplEntry<KE, VN>; | ||
| 66 | |||
| 67 | public: | ||
| 68 | //! Constant value representing no node | ||
| 69 | static constexpr Index NONE = std::numeric_limits<Index>::max(); | ||
| 70 | |||
| 71 | public: | ||
| 72 | //! The index of the parent of this node | ||
| 73 | Index m_parent = NONE; | ||
| 74 | |||
| 75 | //! The index of the left child of this node | ||
| 76 | Index m_left = NONE; | ||
| 77 | |||
| 78 | //! The index of the right child of this node | ||
| 79 | Index m_right = NONE; | ||
| 80 | |||
| 81 | //! The color of this node | ||
| 82 | Color m_color = Color::BLACK; | ||
| 83 | |||
| 84 | //! The set or map entry stored in this node | ||
| 85 | Entry m_entry = {}; | ||
| 86 | |||
| 87 | public: | ||
| 88 | //! Get the child of this node in the specified direction | ||
| 89 | //! \return The child | ||
| 90 | 9838971 | Index getChild(Direction direction //!< The direction | |
| 91 | ) const { | ||
| 92 |
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9838971 | return (direction == Direction::LEFT) ? this->m_left : this->m_right; |
| 93 | } | ||
| 94 | |||
| 95 | //! Set the child of this node in the specified direction | ||
| 96 | 391958 | void setChild(Direction direction, //!< The direction | |
| 97 | Index node //!< The node index | ||
| 98 | ) { | ||
| 99 |
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391958 | if (direction == Direction::LEFT) { |
| 100 | 222081 | this->m_left = node; | |
| 101 | } else { | ||
| 102 | 169877 | this->m_right = node; | |
| 103 | } | ||
| 104 | 391958 | } | |
| 105 | |||
| 106 | public: | ||
| 107 | // Get the opposite direction | ||
| 108 | 215573 | static Direction getOppositeDirection(Direction direction //!< The direction | |
| 109 | ) { | ||
| 110 |
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215573 | return (direction == Direction::LEFT) ? Direction::RIGHT : Direction::LEFT; |
| 111 | } | ||
| 112 | }; | ||
| 113 | |||
| 114 | public: | ||
| 115 | // ---------------------------------------------------------------------- | ||
| 116 | // Type aliases | ||
| 117 | // ---------------------------------------------------------------------- | ||
| 118 | |||
| 119 | //! The color type | ||
| 120 | using Color = typename Node::Color; | ||
| 121 | |||
| 122 | //! The direction type | ||
| 123 | using Direction = typename Node::Direction; | ||
| 124 | |||
| 125 | //! The entry type | ||
| 126 | using Entry = typename Node::Entry; | ||
| 127 | |||
| 128 | //! The node index type | ||
| 129 | using Index = typename Node::Index; | ||
| 130 | |||
| 131 | //! The type of the array for storing the tree nodes | ||
| 132 | using Nodes = ExternalArray<Node>; | ||
| 133 | |||
| 134 | //! The type of the stack of indices of free nodes | ||
| 135 | using FreeNodes = ExternalStack<Index>; | ||
| 136 | |||
| 137 | public: | ||
| 138 | // ---------------------------------------------------------------------- | ||
| 139 | // The ConstIterator type | ||
| 140 | // ---------------------------------------------------------------------- | ||
| 141 | |||
| 142 | //! Const iterator | ||
| 143 | class ConstIterator final : public SetOrMapImplConstIterator<KE, VN> { | ||
| 144 | public: | ||
| 145 | using ImplKind = typename SetOrMapImplConstIterator<KE, VN>::ImplKind; | ||
| 146 | |||
| 147 | public: | ||
| 148 | //! Default constructor | ||
| 149 | 2 | ConstIterator() {} | |
| 150 | |||
| 151 | //! Constructor providing the implementation | ||
| 152 | 129820 | ConstIterator(const RedBlackTreeSetOrMapImpl<KE, VN>& impl) | |
| 153 | 129820 | : SetOrMapImplConstIterator<KE, VN>(), m_impl(&impl) { | |
| 154 |
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129820 | this->m_node = this->m_impl->getOuterNodeUnder(this->m_impl->m_root, Direction::LEFT); |
| 155 | 129820 | } | |
| 156 | |||
| 157 | //! Copy constructor | ||
| 158 | 130077 | ConstIterator(const ConstIterator& it) | |
| 159 | 130077 | : SetOrMapImplConstIterator<KE, VN>(), m_impl(it.m_impl), m_node(it.m_node) {} | |
| 160 | |||
| 161 | //! Destructor | ||
| 162 | 259644 | ~ConstIterator() override = default; | |
| 163 | |||
| 164 | public: | ||
| 165 | //! Copy assignment operator | ||
| 166 | ConstIterator& operator=(const ConstIterator& it) { | ||
| 167 | this->m_impl = it.m_impl; | ||
| 168 | this->m_node = it.m_node; | ||
| 169 | return *this; | ||
| 170 | } | ||
| 171 | |||
| 172 | //! Equality comparison operator | ||
| 173 | 63087 | bool compareEqual(const ConstIterator& it) const { | |
| 174 | 63087 | bool result = false; | |
| 175 |
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63087 | if ((this->m_impl == nullptr) && (it.m_impl == nullptr)) { |
| 176 | 1 | result = true; | |
| 177 |
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63086 | } else if (this->m_impl == it.m_impl) { |
| 178 | 63086 | result |= (this->m_node == it.m_node); | |
| 179 |
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63086 | result |= (!this->isInRange() and !it.isInRange()); |
| 180 | } | ||
| 181 | 63087 | return result; | |
| 182 | } | ||
| 183 | |||
| 184 | //! Return the impl kind | ||
| 185 | //! \return The impl kind | ||
| 186 | 130490 | ImplKind implKind() const override { return ImplKind::RED_BLACK_TREE; } | |
| 187 | |||
| 188 | //! Get the set or map impl entry pointed to by this iterator | ||
| 189 | //! \return The set or map impl entry | ||
| 190 | 2191785 | const Entry& getEntry() const override { return this->m_impl->m_nodes[this->m_node].m_entry; } | |
| 191 | |||
| 192 | //! Increment operator | ||
| 193 | 1068247 | void increment() override { | |
| 194 | 1068247 | FW_ASSERT(this->m_impl != nullptr); | |
| 195 | 1068247 | const auto& nodes = this->m_impl->m_nodes; | |
| 196 |
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1068247 | if (this->m_node != Node::NONE) { |
| 197 | 1068247 | const auto rightChild = nodes[this->m_node].getChild(Direction::RIGHT); | |
| 198 |
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1068247 | if (rightChild != Node::NONE) { |
| 199 | // There is a right child. Go to the leftmost node under that child. | ||
| 200 | 532563 | this->m_node = this->m_impl->getOuterNodeUnder(rightChild, Direction::LEFT); | |
| 201 | } else { | ||
| 202 | // There is no right child. Go upwards until we pass through a left child | ||
| 203 | // or we hit the root. | ||
| 204 | 535684 | const auto capacity = this->m_impl->getCapacity(); | |
| 205 | 535684 | bool done = (capacity == 0); | |
| 206 |
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1068067 | for (FwSizeType i = 0; i < capacity; i++) { |
| 207 | 1068067 | const auto previousNode = this->m_node; | |
| 208 | 1068067 | this->m_node = nodes[this->m_node].m_parent; | |
| 209 |
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2132466 | if ((this->m_node == Node::NONE) or |
| 210 | 1064399 | (nodes[this->m_node].getChild(Direction::LEFT) == previousNode)) { | |
| 211 | 535684 | done = true; | |
| 212 | 535684 | break; | |
| 213 | } | ||
| 214 | } | ||
| 215 | 535684 | FW_ASSERT(done == true); | |
| 216 | } | ||
| 217 | } | ||
| 218 | 1068247 | } | |
| 219 | |||
| 220 | //! Check whether the iterator is in range | ||
| 221 | 2191014 | bool isInRange() const override { | |
| 222 | 2191014 | FW_ASSERT(this->m_impl != nullptr); | |
| 223 | 2191014 | return this->m_node < this->m_impl->getCapacity(); | |
| 224 | } | ||
| 225 | |||
| 226 | //! Set the iterator to the end value | ||
| 227 | 62541 | void setToEnd() { this->m_node = Node::NONE; } | |
| 228 | |||
| 229 | private: | ||
| 230 | //! The implementation over which to iterate | ||
| 231 | const RedBlackTreeSetOrMapImpl<KE, VN>* m_impl = nullptr; | ||
| 232 | |||
| 233 | //! The current node | ||
| 234 | Index m_node = Node::NONE; | ||
| 235 | }; | ||
| 236 | |||
| 237 | public: | ||
| 238 | // ---------------------------------------------------------------------- | ||
| 239 | // Public constructors and destructors | ||
| 240 | // ---------------------------------------------------------------------- | ||
| 241 | |||
| 242 | //! Zero-argument constructor | ||
| 243 |
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635 | RedBlackTreeSetOrMapImpl() = default; |
| 244 | |||
| 245 | //! Constructor providing typed backing storage. | ||
| 246 | //! nodes must point to at least capacity elements of type Node. | ||
| 247 | //! freeNodes must point to at least capacity elements of type FwSizeType. | ||
| 248 | 20 | RedBlackTreeSetOrMapImpl(Node* nodes, //!< The nodes | |
| 249 | Index* freeNodes, //!< The free nodes | ||
| 250 | FwSizeType capacity //!< The capacity | ||
| 251 |
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20 | ) { |
| 252 |
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20 | this->setStorage(nodes, freeNodes, capacity); |
| 253 | 20 | } | |
| 254 | |||
| 255 | //! Constructor providing untyped backing storage. | ||
| 256 | //! data must be aligned according to getByteArrayAlignment(). | ||
| 257 | //! data must contain at least getByteArraySize(capacity) bytes. | ||
| 258 | 1 | RedBlackTreeSetOrMapImpl(ByteArray data, //!< The data | |
| 259 | FwSizeType capacity //!< The capacity | ||
| 260 |
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1 | ) { |
| 261 |
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1 | this->setStorage(data, capacity); |
| 262 | 1 | } | |
| 263 | |||
| 264 | //! Copy constructor | ||
| 265 |
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1 | RedBlackTreeSetOrMapImpl(const RedBlackTreeSetOrMapImpl<KE, VN>& impl) { *this = impl; } |
| 266 | |||
| 267 | //! Destructor | ||
| 268 | 657 | ~RedBlackTreeSetOrMapImpl() = default; | |
| 269 | |||
| 270 | public: | ||
| 271 | // ---------------------------------------------------------------------- | ||
| 272 | // Public member functions | ||
| 273 | // ---------------------------------------------------------------------- | ||
| 274 | |||
| 275 | //! operator= | ||
| 276 | 6 | RedBlackTreeSetOrMapImpl<KE, VN>& operator=(const RedBlackTreeSetOrMapImpl<KE, VN>& impl) { | |
| 277 |
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6 | if (&impl != this) { |
| 278 | 6 | this->m_nodes = impl.m_nodes; | |
| 279 | 6 | this->m_freeNodes = impl.m_freeNodes; | |
| 280 | 6 | this->m_root = impl.m_root; | |
| 281 | } | ||
| 282 | 6 | return *this; | |
| 283 | } | ||
| 284 | |||
| 285 | //! Get the begin iterator | ||
| 286 | 129819 | ConstIterator begin() const { return ConstIterator(*this); } | |
| 287 | |||
| 288 | //! Clear the set or map | ||
| 289 | 2362 | void clear() { | |
| 290 | // Set the root to NONE | ||
| 291 | 2362 | this->m_root = Node::NONE; | |
| 292 | // Clear the free node stack | ||
| 293 | 2362 | this->m_freeNodes.clear(); | |
| 294 | // Push all the nodes on the free node stack | ||
| 295 | 2362 | const auto capacity = this->getCapacity(); | |
| 296 |
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1562768 | for (FwSizeType i = 0; i < capacity; i++) { |
| 297 |
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780203 | const auto status = this->m_freeNodes.push(capacity - i - 1); |
| 298 | 780203 | FW_ASSERT(status == Success::SUCCESS, static_cast<FwAssertArgType>(status)); | |
| 299 | } | ||
| 300 | 2362 | } | |
| 301 | |||
| 302 | //! Get the end iterator | ||
| 303 | 62541 | ConstIterator end() const { | |
| 304 | 62541 | auto it = begin(); | |
| 305 | 62541 | it.setToEnd(); | |
| 306 | 62541 | return it; | |
| 307 | } | ||
| 308 | |||
| 309 | //! Find a value associated with a key in the map or an element in a set | ||
| 310 | //! \return SUCCESS if the item was found | ||
| 311 | 12408 | Success find(const KE& keyOrElement, //!< The key or element | |
| 312 | VN& valueOrNil //!< The value or Nil | ||
| 313 | ) const { | ||
| 314 | 12408 | auto node = Node::NONE; | |
| 315 | 12408 | auto direction = Direction::LEFT; | |
| 316 |
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12408 | const auto status = this->findNode(keyOrElement, node, direction); |
| 317 |
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12408 | if (status == Success::SUCCESS) { |
| 318 |
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4943 | valueOrNil = this->m_nodes[node].m_entry.getValueOrNil(); |
| 319 | } | ||
| 320 | 24816 | return status; | |
| 321 | ✗ | } | |
| 322 | |||
| 323 | //! Get the capacity of the set or map (max number of entries) | ||
| 324 | //! \return The capacity | ||
| 325 | 4310251 | FwSizeType getCapacity() const { return this->m_nodes.getSize(); } | |
| 326 | |||
| 327 | //! Get the size (number of entries) | ||
| 328 | //! \return The size | ||
| 329 | 99934 | FwSizeType getSize() const { | |
| 330 | 99934 | const auto capacity = this->getCapacity(); | |
| 331 | 99934 | const auto freeNodesSize = this->m_freeNodes.getSize(); | |
| 332 | 99934 | FW_ASSERT(freeNodesSize <= capacity, static_cast<FwAssertArgType>(freeNodesSize), | |
| 333 | static_cast<FwAssertArgType>(capacity)); | ||
| 334 | 99934 | return capacity - freeNodesSize; | |
| 335 | } | ||
| 336 | |||
| 337 | //! Insert an element in the set or a (key, value) pair in the map | ||
| 338 | //! \return SUCCESS if there is room in the set or map | ||
| 339 | 83282 | Success insert(const KE& keyOrElement, //!< The key or element | |
| 340 | const VN& valueOrNil //!< The value or Nil | ||
| 341 | ) { | ||
| 342 | 83282 | auto node = Node::NONE; | |
| 343 | 83282 | auto direction = Direction::LEFT; | |
| 344 | 83282 | auto status = Success::FAILURE; | |
| 345 |
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83282 | const auto findStatus = this->findNode(keyOrElement, node, direction); |
| 346 |
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83282 | if (findStatus == Success::SUCCESS) { |
| 347 |
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5057 | this->m_nodes[node].m_entry.setValueOrNil(valueOrNil); |
| 348 | 5057 | status = Success::SUCCESS; | |
| 349 | } else { | ||
| 350 | 78225 | const auto parent = node; | |
| 351 |
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78225 | status = this->m_freeNodes.pop(node); |
| 352 |
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78225 | if (status == Success::SUCCESS) { |
| 353 |
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78220 | this->m_nodes[node] = Node(); |
| 354 |
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78220 | this->m_nodes[node].m_entry.setKeyOrElement(keyOrElement); |
| 355 |
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78220 | this->m_nodes[node].m_entry.setValueOrNil(valueOrNil); |
| 356 |
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78220 | this->insertNode(node, parent, direction); |
| 357 | } | ||
| 358 | } | ||
| 359 |
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166564 | return status; |
| 360 | 83282 | } | |
| 361 | |||
| 362 | //! Remove an element from the set or a (key, value) pair from the map | ||
| 363 | //! \return SUCCESS if the key or element was there | ||
| 364 | 63780 | Success remove(const KE& keyOrElement, //!< The key or element | |
| 365 | VN& valueOrNil //!< The value or Nil | ||
| 366 | ) { | ||
| 367 | 63780 | auto node = Node::NONE; | |
| 368 | 63780 | auto direction = Direction::LEFT; | |
| 369 |
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63780 | const auto status = findNode(keyOrElement, node, direction); |
| 370 |
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63780 | if (status == Success::SUCCESS) { |
| 371 |
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62668 | valueOrNil = this->m_nodes[node].m_entry.getValue(); |
| 372 | 62668 | auto removedNode = Node::NONE; | |
| 373 |
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62668 | this->removeNode(node, removedNode); |
| 374 |
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62668 | const auto pushStatus = this->m_freeNodes.push(removedNode); |
| 375 | 62668 | FW_ASSERT(pushStatus == Success::SUCCESS, static_cast<FwAssertArgType>(pushStatus)); | |
| 376 | 62668 | } | |
| 377 | 127560 | return status; | |
| 378 | ✗ | } | |
| 379 | |||
| 380 | //! Set the backing storage (typed data) | ||
| 381 | //! nodes must point to at least capacity elements of type Node. | ||
| 382 | //! freeNodes must point to at least capacity elements of type FwSizeType. | ||
| 383 | 644 | void setStorage(Node* nodes, //!< The nodes | |
| 384 | Index* freeNodes, //!< The free nodes | ||
| 385 | FwSizeType capacity //!< The capacity | ||
| 386 | ) { | ||
| 387 | 644 | this->m_nodes.setStorage(nodes, capacity); | |
| 388 | 644 | this->m_freeNodes.setStorage(freeNodes, capacity); | |
| 389 | 644 | this->clear(); | |
| 390 | 644 | } | |
| 391 | |||
| 392 | //! Set the backing storage (untyped data) | ||
| 393 | //! data must be aligned according to getByteArrayAlignment(). | ||
| 394 | //! data must contain at least getByteArraySize(capacity) bytes. | ||
| 395 | 3 | void setStorage(ByteArray data, //!< The data | |
| 396 | FwSizeType capacity //!< The capacity | ||
| 397 | ) { | ||
| 398 |
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3 | this->m_nodes.setStorage(data, capacity); |
| 399 | 3 | const auto nodesSize = Nodes::getByteArraySize(capacity); | |
| 400 | // Compute the nearest offset at or after nodesSize that is aligned for FreeNodes | ||
| 401 | 3 | const auto freeNodesAlignment = FreeNodes::getByteArrayAlignment(); | |
| 402 | 3 | const U8 modulus = nodesSize % freeNodesAlignment; | |
| 403 |
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3 | const FwSizeType freeNodesOffset = nodesSize + ((modulus == 0) ? 0 : freeNodesAlignment - modulus); |
| 404 | 3 | FW_ASSERT(freeNodesOffset % freeNodesAlignment == 0, static_cast<FwAssertArgType>(freeNodesOffset), | |
| 405 | static_cast<FwAssertArgType>(freeNodesAlignment)); | ||
| 406 |
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3 | const auto freeNodesSize = FreeNodes::getByteArraySize(capacity); |
| 407 | // Make sure that data has enough room | ||
| 408 | 3 | FW_ASSERT(freeNodesOffset + freeNodesSize <= data.size, static_cast<FwAssertArgType>(freeNodesOffset), | |
| 409 | static_cast<FwAssertArgType>(freeNodesSize), static_cast<FwAssertArgType>(data.size)); | ||
| 410 | 3 | ByteArray freeNodesData(&data.bytes[freeNodesOffset], freeNodesSize); | |
| 411 | // Set the storage and clear freeNodes | ||
| 412 |
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3 | this->m_freeNodes.setStorage(freeNodesData, capacity); |
| 413 |
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3 | this->clear(); |
| 414 | 3 | } | |
| 415 | |||
| 416 | public: | ||
| 417 | // ---------------------------------------------------------------------- | ||
| 418 | // Public static functions | ||
| 419 | // ---------------------------------------------------------------------- | ||
| 420 | |||
| 421 | //! Get the alignment of the storage for a RedBlackTreeSetOrMapImpl | ||
| 422 | //! \return The alignment | ||
| 423 | static constexpr U8 getByteArrayAlignment() { return ExternalArray<Entry>::getByteArrayAlignment(); } | ||
| 424 | |||
| 425 | //! Get the size of the storage for an ExternalArray of the specified capacity, | ||
| 426 | //! as a byte array | ||
| 427 | //! \return The byte array size | ||
| 428 | static constexpr FwSizeType getByteArraySize(FwSizeType capacity //!< The capacity | ||
| 429 | ) { | ||
| 430 | return Nodes::getByteArraySize(capacity) + FreeNodes::getByteArrayAlignment() + | ||
| 431 | FreeNodes::getByteArraySize(capacity); | ||
| 432 | } | ||
| 433 | |||
| 434 | private: | ||
| 435 | // ---------------------------------------------------------------------- | ||
| 436 | // Private helper functions | ||
| 437 | // ---------------------------------------------------------------------- | ||
| 438 | |||
| 439 | //! This function tries to find a node whose key or element ke matches keyOrElement. | ||
| 440 | //! On return from the function: | ||
| 441 | //! 1. If such a node exists, then the return value is SUCCESS, | ||
| 442 | //! and node stores the index of N. | ||
| 443 | //! 2. Otherwise | ||
| 444 | //! a. The return value is FAILURE. | ||
| 445 | //! b. If the tree is empty, then node holds NONE. | ||
| 446 | //! c. Otherwise node stores the index of the node N containing the NONE | ||
| 447 | //! child where ke should be inserted, and direction stores the direction | ||
| 448 | //! of the child in N (left or right). | ||
| 449 | 159470 | Success findNode(const KE& keyOrElement, //!< The key or element (input) | |
| 450 | Index& node, //!< The node index (output) | ||
| 451 | Direction& direction //!< The direction (output) | ||
| 452 | ) const { | ||
| 453 | 159470 | auto result = Success::FAILURE; | |
| 454 | 159470 | auto parent = Node::NONE; | |
| 455 | 159470 | auto child = this->m_root; | |
| 456 |
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159470 | const auto capacity = this->getCapacity(); |
| 457 | 159470 | bool done = (capacity == 0); | |
| 458 |
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994382 | for (FwSizeType i = 0; i < capacity; i++) { |
| 459 |
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994382 | if (child == Node::NONE) { |
| 460 | 86802 | node = parent; | |
| 461 | 86802 | done = true; | |
| 462 | 86802 | break; | |
| 463 | } | ||
| 464 |
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907580 | const auto& entryKey = this->m_nodes[child].m_entry.getKeyOrElement(); |
| 465 |
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907580 | if (keyOrElement == entryKey) { |
| 466 | 72668 | result = Success::SUCCESS; | |
| 467 | 72668 | node = child; | |
| 468 | 72668 | done = true; | |
| 469 | 72668 | break; | |
| 470 |
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834912 | } else if (keyOrElement < entryKey) { |
| 471 | 416848 | direction = Direction::LEFT; | |
| 472 | 416848 | parent = child; | |
| 473 |
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416848 | child = this->m_nodes[parent].m_left; |
| 474 | } else { | ||
| 475 | 418064 | direction = Direction::RIGHT; | |
| 476 | 418064 | parent = child; | |
| 477 |
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418064 | child = this->m_nodes[parent].m_right; |
| 478 | } | ||
| 479 | } | ||
| 480 | 159470 | FW_ASSERT(done); | |
| 481 |
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318940 | return result; |
| 482 | } | ||
| 483 | |||
| 484 | //! Get the direction from the parent, i.e., the direction (left or | ||
| 485 | //! right) to follow from the parent of node to get to node. | ||
| 486 | //! node must not be NONE. The parent of node must not be NONE. | ||
| 487 | 238122 | Direction getDirectionFromParent(Index node //!< The node index | |
| 488 | ) const { | ||
| 489 | 238122 | const auto parent = this->m_nodes[node].m_parent; | |
| 490 | 238122 | const auto parentRight = m_nodes[parent].m_right; | |
| 491 |
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238122 | return (node == parentRight) ? Direction::RIGHT : Direction::LEFT; |
| 492 | } | ||
| 493 | |||
| 494 | //! Get the color of a node | ||
| 495 | //! \return The color | ||
| 496 | 2538006 | Color getNodeColor(Index index //!< The node index | |
| 497 | ) const { | ||
| 498 |
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2538006 | return (index == Node::NONE) ? Color::BLACK : this->m_nodes[index].m_color; |
| 499 | } | ||
| 500 | |||
| 501 | //! Get the outer node under node in the specified direction. If node has | ||
| 502 | //! no child in that direction, then the result is node. | ||
| 503 | 1196463 | Index getOuterNodeUnder(Index node, //!< The node index | |
| 504 | Direction direction //!< The direction | ||
| 505 | ) const { | ||
| 506 |
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1196463 | auto child = (node != Node::NONE) ? this->m_nodes[node].getChild(direction) : Node::NONE; |
| 507 | 1196463 | const auto capacity = this->getCapacity(); | |
| 508 | 1196463 | bool done = (capacity == 0); | |
| 509 |
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2672160 | for (FwSizeType i = 0; i < capacity; i++) { |
| 510 |
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2672159 | if (child == Node::NONE) { |
| 511 | 1196462 | done = true; | |
| 512 | 1196462 | break; | |
| 513 | } | ||
| 514 | 1475697 | node = child; | |
| 515 | 1475697 | child = this->m_nodes[child].getChild(direction); | |
| 516 | } | ||
| 517 | 1196463 | FW_ASSERT(done == true); | |
| 518 | 1196463 | return node; | |
| 519 | } | ||
| 520 | |||
| 521 | //! This function inserts node into the tree as a left or right child of parent, | ||
| 522 | //! according to direction. It rebalances the tree as needed to maintain the | ||
| 523 | //! red-black invariant. | ||
| 524 | //! | ||
| 525 | //! It is permissible for parent to be NONE. In this case we are inserting | ||
| 526 | //! at the root of the tree, and direction is ignored. | ||
| 527 | //! | ||
| 528 | //! It is not permissible for node to be NONE. | ||
| 529 | 78220 | void insertNode(Index node, //!< The node to insert | |
| 530 | Index parent, //!< The new parent | ||
| 531 | Direction direction //!< The direction under the new parent | ||
| 532 | ) { | ||
| 533 | // We assume (1) that the tree is a red-black tree, (2) that parent is NONE or | ||
| 534 | // the child of parent in the direction `direction` is NONE, and (3) that | ||
| 535 | // both children of node are NONE. | ||
| 536 | 78220 | FW_ASSERT(this->m_nodes[node].getChild(Direction::LEFT) == Node::NONE); | |
| 537 | 78220 | FW_ASSERT(this->m_nodes[node].getChild(Direction::RIGHT) == Node::NONE); | |
| 538 | 78220 | this->m_nodes[node].m_color = Color::RED; | |
| 539 | 78220 | this->m_nodes[node].m_parent = parent; | |
| 540 |
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78220 | if (parent == Node::NONE) { |
| 541 | 1411 | this->m_root = node; | |
| 542 | // The tree was empty, and now it consists of a single red node. | ||
| 543 | } else { | ||
| 544 | 76809 | FW_ASSERT(this->m_nodes[parent].getChild(direction) == Node::NONE, | |
| 545 | static_cast<FwAssertArgType>(this->m_nodes[parent].getChild(direction))); | ||
| 546 | // Set the parent | ||
| 547 | 76809 | this->m_nodes[parent].setChild(direction, node); | |
| 548 | 76809 | const auto capacity = this->getCapacity(); | |
| 549 | 76809 | bool done = (capacity == 0); | |
| 550 |
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117798 | for (FwSizeType i = 0; i < capacity; i++) { |
| 551 | // The following invariants hold: (1) node is colored red; (2) | ||
| 552 | // there may be a red child violation from parent to node; and | ||
| 553 | // (3) there are no other violations at any nodes. | ||
| 554 |
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117798 | if (this->getNodeColor(parent) == Color::BLACK) { |
| 555 | // There is no red child violation at parent, because parent is black. | ||
| 556 | 34378 | done = true; | |
| 557 | 34378 | break; | |
| 558 | } | ||
| 559 | 83420 | const auto grandparent = this->m_nodes[parent].m_parent; | |
| 560 |
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83420 | if (grandparent == Node::NONE) { |
| 561 | 2712 | this->m_nodes[parent].m_color = Color::BLACK; | |
| 562 | // This step removes the red child violation at parent. | ||
| 563 | // It preserves all other invariants. | ||
| 564 | 2712 | done = true; | |
| 565 | 2712 | break; | |
| 566 | } | ||
| 567 | 80708 | const auto parentDirection = this->getDirectionFromParent(parent); | |
| 568 | 80708 | const auto parentOppositeDirection = Node::getOppositeDirection(parentDirection); | |
| 569 | 80708 | const auto uncle = this->m_nodes[grandparent].getChild(parentOppositeDirection); | |
| 570 |
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80708 | if (this->getNodeColor(uncle) == Color::BLACK) { |
| 571 |
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37532 | if (this->m_nodes[parent].getChild(parentOppositeDirection) == node) { |
| 572 | // The subtree rooted at grandparent has the following | ||
| 573 | // shape, assuming that parentDirection is RIGHT. | ||
| 574 | // There is a red child violation from parent to node. | ||
| 575 | // There are no other violations at any nodes. | ||
| 576 | // K1, K2, K3, and K4 are arbitrary keys with K1 < K2 < K3 < K4. | ||
| 577 | /* | ||
| 578 | // BBBBBBBBBBBBBBBBBBBB | ||
| 579 | // B B | ||
| 580 | // B K2 (grandparent) B | ||
| 581 | // B B | ||
| 582 | // BBBBBBBBBBBBBBBBBBBB | ||
| 583 | // / \ | ||
| 584 | // / \ | ||
| 585 | // V V | ||
| 586 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRR | ||
| 587 | // B B R R | ||
| 588 | // B K1 (uncle) B R K4 (parent) R | ||
| 589 | // B B R R | ||
| 590 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRR | ||
| 591 | // | | / \ | ||
| 592 | // | | / \ | ||
| 593 | // V V V \ | ||
| 594 | // ------------------ RRRRRRRRRRRRR | | ||
| 595 | // | | R R | | ||
| 596 | // | black height n | R K3 (node) R | | ||
| 597 | // | | R R | | ||
| 598 | // ------------------ RRRRRRRRRRRRR / | ||
| 599 | // | | / | ||
| 600 | // | | / | ||
| 601 | // V V V | ||
| 602 | // ---------------------- | ||
| 603 | // | | | ||
| 604 | // | black height n + 1 | | ||
| 605 | // | | | ||
| 606 | // ---------------------- | ||
| 607 | */ | ||
| 608 | 11554 | this->rotateSubtree(parent, parentDirection); | |
| 609 | 11554 | parent = this->m_nodes[grandparent].getChild(parentDirection); | |
| 610 | } | ||
| 611 | // The subtree rooted at grandparent has the following | ||
| 612 | // shape, assuming that parentDirection is RIGHT. | ||
| 613 | // There is a red child violation from parent to K4. | ||
| 614 | // There are no other violations at any nodes. | ||
| 615 | /* | ||
| 616 | // BBBBBBBBBBBBBBBBBBBB | ||
| 617 | // B B | ||
| 618 | // B K2 (grandparent) B | ||
| 619 | // B B | ||
| 620 | // BBBBBBBBBBBBBBBBBBBB | ||
| 621 | // / \ | ||
| 622 | // / \ | ||
| 623 | // V V | ||
| 624 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRR | ||
| 625 | // B B R R | ||
| 626 | // B K1 (uncle) B R K3 (parent) R | ||
| 627 | // B B R R | ||
| 628 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRR | ||
| 629 | // | | / \ | ||
| 630 | // | | / \ | ||
| 631 | // V V | V | ||
| 632 | // ------------------ | RRRRRRRRRRRRRR | ||
| 633 | // | | | R R | ||
| 634 | // | black height n | | R K4 R | ||
| 635 | // | | | R R | ||
| 636 | // ------------------ | RRRRRRRRRRRRRR | ||
| 637 | // \ | | | ||
| 638 | // \ | | | ||
| 639 | // V V V | ||
| 640 | // ---------------------- | ||
| 641 | // | | | ||
| 642 | // | black height n + 1 | | ||
| 643 | // | | | ||
| 644 | // ---------------------- | ||
| 645 | */ | ||
| 646 | 37532 | this->rotateSubtree(grandparent, parentOppositeDirection); | |
| 647 | 37532 | this->m_nodes[parent].m_color = Color::BLACK; | |
| 648 | 37532 | this->m_nodes[grandparent].m_color = Color::RED; | |
| 649 | // The subtree has the following shape. | ||
| 650 | /* | ||
| 651 | // BBBBBBBBBBBBBBBBBBB | ||
| 652 | // B B | ||
| 653 | // B K3 (parent) B | ||
| 654 | // B B | ||
| 655 | // BBBBBBBBBBBBBBBBBBB | ||
| 656 | // / \ | ||
| 657 | // / \ | ||
| 658 | // V V | ||
| 659 | // RRRRRRRRRRRRRRRRRRRR RRRRRRRRRRRRRRRR | ||
| 660 | // R R R R | ||
| 661 | // R K2 (grandparent) R R K4 R | ||
| 662 | // R R R R | ||
| 663 | // RRRRRRRRRRRRRRRRRRRR RRRRRRRRRRRRRRRR | ||
| 664 | // / \ | | | ||
| 665 | // / \ | | | ||
| 666 | // V V V V | ||
| 667 | // BBBBBBBBBBBBBBBBBB ---------------------------- | ||
| 668 | // B B | | | ||
| 669 | // B K1 (uncle) B | black height n + 1 | | ||
| 670 | // B B | | | ||
| 671 | // BBBBBBBBBBBBBBBBBB ---------------------------- | ||
| 672 | // | | | ||
| 673 | // | | | ||
| 674 | // V V | ||
| 675 | // ------------------ | ||
| 676 | // | | | ||
| 677 | // | black height n | | ||
| 678 | // | | | ||
| 679 | // ------------------ | ||
| 680 | */ | ||
| 681 | 37532 | done = true; | |
| 682 | 37532 | break; | |
| 683 | } else { | ||
| 684 | // The subtree rooted at grandparent has one of four | ||
| 685 | // shapes, one of which is shown below. Each of the arrows | ||
| 686 | // to red nodes may point the other way. | ||
| 687 | // There is a red child violation from parent to K4. | ||
| 688 | // There are no other violations at any nodes. | ||
| 689 | /* | ||
| 690 | // BBBBBBBBBBBBBBBBBBBB | ||
| 691 | // B B | ||
| 692 | // B K2 (grandparent) B | ||
| 693 | // B B | ||
| 694 | // BBBBBBBBBBBBBBBBBBBB | ||
| 695 | // / \ | ||
| 696 | // / \ | ||
| 697 | // V V | ||
| 698 | // RRRRRRRRRRRRRR RRRRRRRRRRRRRRR | ||
| 699 | // R R R R | ||
| 700 | // R K1 (uncle) R R K3 (parent) R | ||
| 701 | // R R R R | ||
| 702 | // RRRRRRRRRRRRRR RRRRRRRRRRRRRRR | ||
| 703 | // \ \ / \ | ||
| 704 | // \ \ / \ | ||
| 705 | // \ \ / V | ||
| 706 | // \ \ / RRRRRRRRRRRRRR | ||
| 707 | // \ \ / R R | ||
| 708 | // \ \ / R K4 R | ||
| 709 | // \ \ | R R | ||
| 710 | // \ \ | RRRRRRRRRRRRRR | ||
| 711 | // \ \ | / / | ||
| 712 | // \ \ | / / | ||
| 713 | // V V V V V | ||
| 714 | // ---------------------------------- | ||
| 715 | // | | | ||
| 716 | // | black height n | | ||
| 717 | // | | | ||
| 718 | // ---------------------------------- | ||
| 719 | */ | ||
| 720 | 43176 | this->m_nodes[parent].m_color = Color::BLACK; | |
| 721 | 43176 | this->m_nodes[uncle].m_color = Color::BLACK; | |
| 722 | 43176 | this->m_nodes[grandparent].m_color = Color::RED; | |
| 723 | 43176 | node = grandparent; | |
| 724 | 43176 | parent = this->m_nodes[node].m_parent; | |
| 725 | // The tree shown above now has the following shape. | ||
| 726 | /* | ||
| 727 | // ??????????????????? | ||
| 728 | // ? ? | ||
| 729 | // ? parent ? | ||
| 730 | // ? ? | ||
| 731 | // ??????????????????? | ||
| 732 | // ^ | ||
| 733 | // | | ||
| 734 | // | | ||
| 735 | // RRRRRRRRRRRRRRRRRRR | ||
| 736 | // R R | ||
| 737 | // R K2 (node) R | ||
| 738 | // R R | ||
| 739 | // RRRRRRRRRRRRRRRRRRR | ||
| 740 | // / \ | ||
| 741 | // / \ | ||
| 742 | // V V | ||
| 743 | // BBBBBBBBBBBBBB BBBBBBBBBBBBBBB | ||
| 744 | // B B B B | ||
| 745 | // B K1 (uncle) B B K3 B | ||
| 746 | // B B B B | ||
| 747 | // BBBBBBBBBBBBBB BBBBBBBBBBBBBBB | ||
| 748 | // \ \ / \ | ||
| 749 | // \ \ / \ | ||
| 750 | // \ \ / V | ||
| 751 | // \ \ / RRRRRRRRRRRRRR | ||
| 752 | // \ \ / R R | ||
| 753 | // \ \ / R K4 R | ||
| 754 | // \ \ | R R | ||
| 755 | // \ \ | RRRRRRRRRRRRRR | ||
| 756 | // \ \ | / / | ||
| 757 | // \ \ | / / | ||
| 758 | // V V V V V | ||
| 759 | // ---------------------------------- | ||
| 760 | // | | | ||
| 761 | // | black height n | | ||
| 762 | // | | | ||
| 763 | // ---------------------------------- | ||
| 764 | */ | ||
| 765 |
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43176 | if (parent == Node::NONE) { |
| 766 | // We have reached the root of the tree. | ||
| 767 | // Break out of the loop. | ||
| 768 | 2187 | done = true; | |
| 769 | 2187 | break; | |
| 770 | } | ||
| 771 | // The invariants at the top of the loop are satisfied. | ||
| 772 | // Continue to the next iteration. | ||
| 773 | } | ||
| 774 | } | ||
| 775 | 76809 | FW_ASSERT(done); | |
| 776 | } | ||
| 777 | // The tree is a red-black tree. | ||
| 778 | 78220 | } | |
| 779 | |||
| 780 | //! This function removes a node that is colored black and is a leaf node | ||
| 781 | //! (i.e., it has no children) and is not the root. node stores the node to | ||
| 782 | //! remove. It must not be NONE. | ||
| 783 | 34335 | void removeBlackLeafNode(Index node //!< The node to remove | |
| 784 | ) { | ||
| 785 | // We assume that the tree is a red-black tree, that node is colored | ||
| 786 | // black, that node is a leaf node, and that node is not the root. | ||
| 787 | 34335 | auto parent = m_nodes[node].m_parent; | |
| 788 | // Since node is not the root, parent is not NONE. | ||
| 789 | 34335 | auto direction = this->getDirectionFromParent(node); | |
| 790 | 34335 | auto oppositeDirection = Node::getOppositeDirection(direction); | |
| 791 | // The leaf-augmented subtree rooted at parent has this shape, assuming | ||
| 792 | // direction == RIGHT. We use ? to represent the unknown color (red or | ||
| 793 | // black) of parent. | ||
| 794 | /* | ||
| 795 | // ???????????????? | ||
| 796 | // ? ? | ||
| 797 | // ? parent ? | ||
| 798 | // ? ? | ||
| 799 | // ???????????????? | ||
| 800 | // / \ | ||
| 801 | // / \ | ||
| 802 | // V V | ||
| 803 | // ------------------ BBBBBBBBBBBB | ||
| 804 | // | | B B | ||
| 805 | // | black height 2 | B node B | ||
| 806 | // | | B B | ||
| 807 | // ------------------ BBBBBBBBBBBB | ||
| 808 | // / \ | ||
| 809 | // / \ | ||
| 810 | // V V | ||
| 811 | // BBBBBBBBBB BBBBBBBBBB | ||
| 812 | // B B B B | ||
| 813 | // B B B B | ||
| 814 | // B B B B | ||
| 815 | // BBBBBBBBBB BBBBBBBBBB | ||
| 816 | */ | ||
| 817 | 34335 | this->m_nodes[parent].setChild(direction, Node::NONE); | |
| 818 | // The previous step performs the deletion. | ||
| 819 | // The remaining steps are for rebalancing. | ||
| 820 | /* | ||
| 821 | // The leaf-augmented subtree rooted at parent looks like this, | ||
| 822 | // assuming direction == RIGHT: | ||
| 823 | // | ||
| 824 | // ???????????????? | ||
| 825 | // ? ? | ||
| 826 | // ? parent ? | ||
| 827 | // ? ? | ||
| 828 | // ???????????????? | ||
| 829 | // / \ | ||
| 830 | // / \ | ||
| 831 | // V V | ||
| 832 | // ------------------ BBBBBBBBBBBB | ||
| 833 | // | | B B | ||
| 834 | // | black height 2 | B B | ||
| 835 | // | | B B | ||
| 836 | // ------------------ BBBBBBBBBBBB | ||
| 837 | // | ||
| 838 | // The black height invariant is violated, because the left subtree of | ||
| 839 | // parent has black height 2, and the right subtree has black height 1. | ||
| 840 | // Therefore there is a black height violation at parent and at every | ||
| 841 | // node in the path from the root to parent. To restore the black | ||
| 842 | // height invariant, we must perform rebalancing. | ||
| 843 | */ | ||
| 844 | 34335 | bool done = false; | |
| 845 | 34335 | const auto capacity = this->getCapacity(); | |
| 846 |
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48733 | for (FwSizeType i = 0; i < capacity; i++) { |
| 847 | // The red child constraint is satisfied. The black height | ||
| 848 | // constraint is violated because the leaf-augmented subtree rooted | ||
| 849 | // at parent has this shape, assuming direction == RIGHT. i is the | ||
| 850 | // loop index. Note that this diagram agrees with the previous one | ||
| 851 | // when i = 0. | ||
| 852 | /* | ||
| 853 | // ???????????????? | ||
| 854 | // ? ? | ||
| 855 | // ? parent ? | ||
| 856 | // ? ? | ||
| 857 | // ???????????????? | ||
| 858 | // / \ | ||
| 859 | // / \ | ||
| 860 | // V V | ||
| 861 | // ---------------------- ---------------------- | ||
| 862 | // | | | | | ||
| 863 | // | black height i + 2 | | black height i + 1 | | ||
| 864 | // | | | | | ||
| 865 | // ---------------------- ---------------------- | ||
| 866 | // | ||
| 867 | // The black height constraint would be satisfied if the child of | ||
| 868 | // parent in the direction `direction` were replaced with a red-black | ||
| 869 | // tree of black height i + 2. | ||
| 870 | */ | ||
| 871 |
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|
48733 | auto sibling = this->m_nodes[parent].getChild(oppositeDirection); |
| 872 |
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48733 | auto closeNephew = this->m_nodes[sibling].getChild(direction); |
| 873 |
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48733 | auto distantNephew = this->m_nodes[sibling].getChild(oppositeDirection); |
| 874 | // The leaf-augmented subtree rooted at parent has this shape | ||
| 875 | // (direction == RIGHT). If distantNephew or closeNephew are leaves | ||
| 876 | // in the leaf-augmented tree, then K1 and K4 are names for the | ||
| 877 | // nodes; they are not keys in the original tree. | ||
| 878 | // There is a black height violation at parent. | ||
| 879 | /* | ||
| 880 | // ??????????????????? | ||
| 881 | // ? ? | ||
| 882 | // ? K6 (parent) ? | ||
| 883 | // ? ? | ||
| 884 | // ??????????????????? | ||
| 885 | // / \ | ||
| 886 | // / \ | ||
| 887 | // V V | ||
| 888 | // ????????????????? ---------------------- | ||
| 889 | // ? ? | | | ||
| 890 | // ? K2 (sibling) ? | black height i + 1 | | ||
| 891 | // ? ? | | | ||
| 892 | // ????????????????? ---------------------- | ||
| 893 | // / \ | ||
| 894 | // / \ | ||
| 895 | // V V | ||
| 896 | // ???????????????????? ???????????????????? | ||
| 897 | // ? ? ? ? | ||
| 898 | // ? K1 (distantNephew) ? ? K4 (closeNephew) ? | ||
| 899 | // ? ? ? ? | ||
| 900 | // ???????????????????? ???????????????????? | ||
| 901 | // | | | | | ||
| 902 | // | | | | | ||
| 903 | // V V V V | ||
| 904 | // ------------------------- ------------------------- | ||
| 905 | // | | | | | ||
| 906 | // | black height i + 2 - | | black height i + 2 - | | ||
| 907 | // | number of black nodes | | number of black nodes | | ||
| 908 | // | in { K1, K2 } | | in { K2, K4 } | | ||
| 909 | // | | | | | ||
| 910 | // ------------------------- ------------------------- | ||
| 911 | */ | ||
| 912 |
3/3✓ Branch 2 taken 48733 times.
✓ Branch 4 taken 11486 times.
✓ Branch 5 taken 37247 times.
|
48733 | if (this->getNodeColor(sibling) == Color::RED) { |
| 913 | // The leaf-augmented subtree rooted at parent has this shape. | ||
| 914 | // There is a black height violation at parent. | ||
| 915 | /* | ||
| 916 | // BBBBBBBBBBBBBBBBBBB | ||
| 917 | // B B | ||
| 918 | // B K6 (parent) B | ||
| 919 | // B B | ||
| 920 | // BBBBBBBBBBBBBBBBBBB | ||
| 921 | // / \ | ||
| 922 | // / \ | ||
| 923 | // V V | ||
| 924 | // RRRRRRRRRRRRRRRRR ---------------------- | ||
| 925 | // R R | | | ||
| 926 | // R K2 (sibling) R | black height i + 1 | | ||
| 927 | // R R | | | ||
| 928 | // RRRRRRRRRRRRRRRRR ---------------------- | ||
| 929 | // / \ | ||
| 930 | // / \ | ||
| 931 | // V V | ||
| 932 | // BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB | ||
| 933 | // B B B B | ||
| 934 | // B K1 (distantNephew) B B K4 (closeNephew) B | ||
| 935 | // B B B B | ||
| 936 | // BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB | ||
| 937 | // | | | | | ||
| 938 | // | | | | | ||
| 939 | // V V V V | ||
| 940 | // ------------------------ ------------------------ | ||
| 941 | // | | | | | ||
| 942 | // | black height i + 1 | | black height i + 1 | | ||
| 943 | // | | | | | ||
| 944 | // ------------------------ ------------------------ | ||
| 945 | */ | ||
| 946 |
1/1✓ Branch 2 taken 11486 times.
|
11486 | this->rotateSubtree(parent, direction); |
| 947 |
1/1✓ Branch 3 taken 11486 times.
|
11486 | this->m_nodes[parent].m_color = Color::RED; |
| 948 |
1/1✓ Branch 3 taken 11486 times.
|
11486 | this->m_nodes[sibling].m_color = Color::BLACK; |
| 949 | 11486 | sibling = closeNephew; | |
| 950 |
1/1✓ Branch 3 taken 11486 times.
|
11486 | closeNephew = this->m_nodes[sibling].getChild(direction); |
| 951 |
1/1✓ Branch 3 taken 11486 times.
|
11486 | distantNephew = this->m_nodes[sibling].getChild(oppositeDirection); |
| 952 | // The subtree has this shape: | ||
| 953 | /* | ||
| 954 | // BBBBBBBBBBBBBBBB | ||
| 955 | // B B | ||
| 956 | // B K2 B | ||
| 957 | // B B | ||
| 958 | // BBBBBBBBBBBBBBBB | ||
| 959 | // / \ | ||
| 960 | // / \ | ||
| 961 | // / \ | ||
| 962 | // V V | ||
| 963 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRRRRRR | ||
| 964 | // B B R R | ||
| 965 | // B K1 B R K6 (parent) R | ||
| 966 | // B B R R | ||
| 967 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRRRRRR | ||
| 968 | // | | / \ | ||
| 969 | // | | / \ | ||
| 970 | // V V V V | ||
| 971 | // ------------------------ BBBBBBBBBBBBBBBBBB ------------------------ | ||
| 972 | // | | B B | | | ||
| 973 | // | black height i + 1 | B K4 (sibling) B | black height i + 1 | | ||
| 974 | // | | B B | | | ||
| 975 | // ------------------------ BBBBBBBBBBBBBBBBBB ------------------------ | ||
| 976 | // / \ | ||
| 977 | // / \ | ||
| 978 | // V V | ||
| 979 | // -------------------------------- -------------------------------- | ||
| 980 | // | | | | | ||
| 981 | // | black height i + 1 | | black height i + 1 | | ||
| 982 | // | with root K3 (distantNephew) | | with root K5 (closeNephew) | | ||
| 983 | // | | | | | ||
| 984 | // -------------------------------- -------------------------------- | ||
| 985 | */ | ||
| 986 |
3/3✓ Branch 2 taken 11486 times.
✓ Branch 4 taken 5352 times.
✓ Branch 5 taken 6134 times.
|
11486 | if (this->getNodeColor(distantNephew) == Color::RED) { |
| 987 | // The subtree has this shape: | ||
| 988 | /* | ||
| 989 | // BBBBBBBBBBBBBBBB | ||
| 990 | // B B | ||
| 991 | // B K2 B | ||
| 992 | // B B | ||
| 993 | // BBBBBBBBBBBBBBBB | ||
| 994 | // / \ | ||
| 995 | // / \ | ||
| 996 | // / \ | ||
| 997 | // V V | ||
| 998 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRRRRRR | ||
| 999 | // B B R R | ||
| 1000 | // B K1 B R K6 (parent) R | ||
| 1001 | // B B R R | ||
| 1002 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRRRRRR | ||
| 1003 | // | | / \ | ||
| 1004 | // | | / \ | ||
| 1005 | // V V V V | ||
| 1006 | // ------------------------ BBBBBBBBBBBBBBBBBB ------------------------ | ||
| 1007 | // | | B B | | | ||
| 1008 | // | black height i + 1 | B K4 (sibling) B | black height i + 1 | | ||
| 1009 | // | | B B | | | ||
| 1010 | // ------------------------ BBBBBBBBBBBBBBBBBB ------------------------ | ||
| 1011 | // / \ | ||
| 1012 | // / \ | ||
| 1013 | // V V | ||
| 1014 | // RRRRRRRRRRRRRRRRRRRRRRRRRR ------------------------ | ||
| 1015 | // R R | | | ||
| 1016 | // R K3 (distantNephew) R | black height i + 1 | | ||
| 1017 | // R R | | | ||
| 1018 | // RRRRRRRRRRRRRRRRRRRRRRRRRR ------------------------ | ||
| 1019 | // | | | ||
| 1020 | // | | | ||
| 1021 | // V V | ||
| 1022 | // ------------------------ | ||
| 1023 | // | | | ||
| 1024 | // | black height i + 1 | | ||
| 1025 | // | | | ||
| 1026 | // ------------------------ | ||
| 1027 | */ | ||
| 1028 |
1/1✓ Branch 2 taken 5352 times.
|
5352 | this->removeBlackLeafNodeHelper2(parent, sibling, distantNephew, direction); |
| 1029 | // The subtree has this shape. The entire tree is a valid red-black tree. | ||
| 1030 | /* | ||
| 1031 | // BBBBBBBBBBBBBBBB | ||
| 1032 | // B B | ||
| 1033 | // B K2 B | ||
| 1034 | // B B | ||
| 1035 | // BBBBBBBBBBBBBBBB | ||
| 1036 | // / \ | ||
| 1037 | // / \ | ||
| 1038 | // / \ | ||
| 1039 | // V V | ||
| 1040 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRRRRRR | ||
| 1041 | // B B R R | ||
| 1042 | // B K1 B R K4 (sibling) R | ||
| 1043 | // B B R R | ||
| 1044 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRRRRRR | ||
| 1045 | // | | / \ | ||
| 1046 | // | | / \ | ||
| 1047 | // V V V V | ||
| 1048 | // ------------------------ BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBB | ||
| 1049 | // | | B B B B | ||
| 1050 | // | black height i + 1 | B K3 (distantNephew) B B K6 (parent) B | ||
| 1051 | // | | B B B B | ||
| 1052 | // ------------------------ BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBB | ||
| 1053 | // | | | | | ||
| 1054 | // | | | | | ||
| 1055 | // V V V V | ||
| 1056 | // ------------------------ ------------------------ | ||
| 1057 | // | | | | | ||
| 1058 | // | black height i + 1 | | black height i + 1 | | ||
| 1059 | // | | | | | ||
| 1060 | // ------------------------ ------------------------ | ||
| 1061 | */ | ||
| 1062 | 5352 | done = true; | |
| 1063 | 5352 | break; | |
| 1064 |
3/3✓ Branch 2 taken 6134 times.
✓ Branch 4 taken 2306 times.
✓ Branch 5 taken 3828 times.
|
6134 | } else if (this->getNodeColor(closeNephew) == Color::RED) { |
| 1065 | // The subtree has this shape: | ||
| 1066 | /* | ||
| 1067 | // BBBBBBBBBBBBBBBB | ||
| 1068 | // B B | ||
| 1069 | // B K2 B | ||
| 1070 | // B B | ||
| 1071 | // BBBBBBBBBBBBBBBB | ||
| 1072 | // / \ | ||
| 1073 | // / \ | ||
| 1074 | // / \ | ||
| 1075 | // V V | ||
| 1076 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRRRRRR | ||
| 1077 | // B B R R | ||
| 1078 | // B K1 B R K6 (parent) R | ||
| 1079 | // B B R R | ||
| 1080 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRRRRRR | ||
| 1081 | // | | / \ | ||
| 1082 | // | | / \ | ||
| 1083 | // V V V V | ||
| 1084 | // ------------------------ BBBBBBBBBBBBBBBBBB ------------------------ | ||
| 1085 | // | | B B | | | ||
| 1086 | // | black height i + 1 | B K4 (sibling) B | black height i + 1 | | ||
| 1087 | // | | B B | | | ||
| 1088 | // ------------------------ BBBBBBBBBBBBBBBBBB ------------------------ | ||
| 1089 | // / \ | ||
| 1090 | // / \ | ||
| 1091 | // V V | ||
| 1092 | // ------------------------ RRRRRRRRRRRRRRRRRRRRRRRRRR | ||
| 1093 | // | | R R | ||
| 1094 | // | black height i + 1 | R K5 (closeNephew) R | ||
| 1095 | // | | R R | ||
| 1096 | // ------------------------ RRRRRRRRRRRRRRRRRRRRRRRRRR | ||
| 1097 | // | | | ||
| 1098 | // | | | ||
| 1099 | // V V | ||
| 1100 | // ------------------------ | ||
| 1101 | // | | | ||
| 1102 | // | black height i + 1 | | ||
| 1103 | // | | | ||
| 1104 | // ------------------------ | ||
| 1105 | */ | ||
| 1106 |
1/1✓ Branch 2 taken 2306 times.
|
2306 | this->removeBlackLeafNodeHelper1(closeNephew, oppositeDirection, sibling, distantNephew); |
| 1107 | // The subtree has this shape: | ||
| 1108 | /* | ||
| 1109 | // BBBBBBBBBBBBBBBB | ||
| 1110 | // B B | ||
| 1111 | // B K2 B | ||
| 1112 | // B B | ||
| 1113 | // BBBBBBBBBBBBBBBB | ||
| 1114 | // / \ | ||
| 1115 | // / \ | ||
| 1116 | // / \ | ||
| 1117 | // V V | ||
| 1118 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRRRRRR | ||
| 1119 | // B B R R | ||
| 1120 | // B K1 B R K6 (parent) R | ||
| 1121 | // B B R R | ||
| 1122 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRRRRRR | ||
| 1123 | // | | / \ | ||
| 1124 | // | | / \ | ||
| 1125 | // V V V V | ||
| 1126 | // ------------------------ BBBBBBBBBBBBBBBBBB ------------------------ | ||
| 1127 | // | | B B | | | ||
| 1128 | // | black height i + 1 | B K5 (sibling) B | black height i + 1 | | ||
| 1129 | // | | B B | | | ||
| 1130 | // ------------------------ BBBBBBBBBBBBBBBBBB ------------------------ | ||
| 1131 | // / \ | ||
| 1132 | // / \ | ||
| 1133 | // V V | ||
| 1134 | // RRRRRRRRRRRRRRRRRRRRRRRRRR ------------------------ | ||
| 1135 | // R R | | | ||
| 1136 | // R K4 (distantNephew) R | black height i + 1 | | ||
| 1137 | // R R | | | ||
| 1138 | // RRRRRRRRRRRRRRRRRRRRRRRRRR ------------------------ | ||
| 1139 | // | | | ||
| 1140 | // | | | ||
| 1141 | // V V | ||
| 1142 | // ------------------------ | ||
| 1143 | // | | | ||
| 1144 | // | black height i + 1 | | ||
| 1145 | // | | | ||
| 1146 | // ----------------------- | ||
| 1147 | */ | ||
| 1148 |
1/1✓ Branch 2 taken 2306 times.
|
2306 | this->removeBlackLeafNodeHelper2(parent, sibling, distantNephew, direction); |
| 1149 | // The subtree has this shape. The entire tree is a valid red-black tree. | ||
| 1150 | /* | ||
| 1151 | // BBBBBBBBBBBBBBBB | ||
| 1152 | // B B | ||
| 1153 | // B K2 B | ||
| 1154 | // B B | ||
| 1155 | // BBBBBBBBBBBBBBBB | ||
| 1156 | // / \ | ||
| 1157 | // / \ | ||
| 1158 | // / \ | ||
| 1159 | // V V | ||
| 1160 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRRRRRRR | ||
| 1161 | // B B R R | ||
| 1162 | // B K1 B R K5 (sibling) R | ||
| 1163 | // B B R R | ||
| 1164 | // BBBBBBBBBBBBBB RRRRRRRRRRRRRRRRRRRR | ||
| 1165 | // | | / \ | ||
| 1166 | // | | / \ | ||
| 1167 | // V V V V | ||
| 1168 | // ------------------------ BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBB | ||
| 1169 | // | | B B B B | ||
| 1170 | // | black height i + 1 | B K4 (distantNephew) B B K6 (parent) B | ||
| 1171 | // | | B B B B | ||
| 1172 | // ------------------------ BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBB | ||
| 1173 | // | | | | | ||
| 1174 | // | | | | | ||
| 1175 | // V V V V | ||
| 1176 | // ------------------------ ------------------------ | ||
| 1177 | // | | | | | ||
| 1178 | // | black height i + 1 | | black height i + 1 | | ||
| 1179 | // | | | | | ||
| 1180 | // ------------------------ ------------------------ | ||
| 1181 | */ | ||
| 1182 | 2306 | done = true; | |
| 1183 | 2306 | break; | |
| 1184 | } else { | ||
| 1185 |
1/1✓ Branch 3 taken 3828 times.
|
3828 | this->m_nodes[sibling].m_color = Color::RED; |
| 1186 |
1/1✓ Branch 3 taken 3828 times.
|
3828 | this->m_nodes[parent].m_color = Color::BLACK; |
| 1187 | // The subtree has this shape. The entire tree is a valid red-black tree. | ||
| 1188 | /* | ||
| 1189 | // BBBBBBBBBBBBBBBB | ||
| 1190 | // B B | ||
| 1191 | // B K2 B | ||
| 1192 | // B B | ||
| 1193 | // BBBBBBBBBBBBBBBB | ||
| 1194 | // / \ | ||
| 1195 | // / \ | ||
| 1196 | // / \ | ||
| 1197 | // V V | ||
| 1198 | // BBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBB | ||
| 1199 | // B B B B | ||
| 1200 | // B K1 B B K6 (parent) B | ||
| 1201 | // B B B B | ||
| 1202 | // BBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBB | ||
| 1203 | // | | / \ | ||
| 1204 | // | | / \ | ||
| 1205 | // V V V V | ||
| 1206 | // ------------------------ RRRRRRRRRRRRRRRRRR ------------------------ | ||
| 1207 | // | | R R | | | ||
| 1208 | // | black height i + 1 | R K4 (sibling) R | black height i + 1 | | ||
| 1209 | // | | R R | | | ||
| 1210 | // ------------------------ RRRRRRRRRRRRRRRRRR ------------------------ | ||
| 1211 | // / \ | ||
| 1212 | // / \ | ||
| 1213 | // V V | ||
| 1214 | // BBBBBBBBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBBBBBB | ||
| 1215 | // B B B B | ||
| 1216 | // B K3 (distantNephew) B B K5 (closeNephew) B | ||
| 1217 | // B B B B | ||
| 1218 | // BBBBBBBBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBBBBBB | ||
| 1219 | // | | | | | ||
| 1220 | // | | | | | ||
| 1221 | // V V V V | ||
| 1222 | // ------------------------ ------------------------ | ||
| 1223 | // | | | | | ||
| 1224 | // | black height i | | black height i | | ||
| 1225 | // | | | | | ||
| 1226 | // ------------------------ ------------------------ | ||
| 1227 | */ | ||
| 1228 | 3828 | done = true; | |
| 1229 | 3828 | break; | |
| 1230 | } | ||
| 1231 |
3/3✓ Branch 2 taken 37247 times.
✓ Branch 4 taken 8704 times.
✓ Branch 5 taken 28543 times.
|
37247 | } else if (this->getNodeColor(distantNephew) == Color::RED) { |
| 1232 | // The leaf-augmented subtree rooted at parent has this shape. | ||
| 1233 | // There is a black height violation at parent. | ||
| 1234 | /* | ||
| 1235 | // ??????????????????? | ||
| 1236 | // ? ? | ||
| 1237 | // ? K6 (parent) ? | ||
| 1238 | // ? ? | ||
| 1239 | // ??????????????????? | ||
| 1240 | // / \ | ||
| 1241 | // / \ | ||
| 1242 | // V V | ||
| 1243 | // BBBBBBBBBBBBBBBBB ---------------------- | ||
| 1244 | // B B | | | ||
| 1245 | // B K2 (sibling) B | black height i + 1 | | ||
| 1246 | // B B | | | ||
| 1247 | // BBBBBBBBBBBBBBBBB ---------------------- | ||
| 1248 | // / \ | ||
| 1249 | // / \ | ||
| 1250 | // V V | ||
| 1251 | // RRRRRRRRRRRRRRRRRRRR ------------------------ | ||
| 1252 | // R R | | | ||
| 1253 | // R K1 (distantNephew) R | black height i + 1 | | ||
| 1254 | // R R | | | ||
| 1255 | // RRRRRRRRRRRRRRRRRRRR ------------------------ | ||
| 1256 | // | | | ||
| 1257 | // | | | ||
| 1258 | // V V | ||
| 1259 | // ------------------------ | ||
| 1260 | // | | | ||
| 1261 | // | black height i + 1 | | ||
| 1262 | // | | | ||
| 1263 | // ------------------------ | ||
| 1264 | */ | ||
| 1265 |
1/1✓ Branch 2 taken 8704 times.
|
8704 | this->removeBlackLeafNodeHelper2(parent, sibling, distantNephew, direction); |
| 1266 | // The subtree has this shape. The entire tree is a valid red-black tree. | ||
| 1267 | /* | ||
| 1268 | // BBBBBBBBBBBBBBBBB | ||
| 1269 | // B B | ||
| 1270 | // B K2 (sibling) B | ||
| 1271 | // B B | ||
| 1272 | // BBBBBBBBBBBBBBBBB | ||
| 1273 | // / \ | ||
| 1274 | // / \ | ||
| 1275 | // V V | ||
| 1276 | // BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBB | ||
| 1277 | // B B B B | ||
| 1278 | // B K1 (distantNephew) B B K6 (parent) B | ||
| 1279 | // B B B B | ||
| 1280 | // RRRRRRRRRRRRRRRRRRRR BBBBBBBBBBBBBBBBB | ||
| 1281 | // | | | | | ||
| 1282 | // | | | | | ||
| 1283 | // V V V V | ||
| 1284 | // ------------------------ ------------------------ | ||
| 1285 | // | | | | | ||
| 1286 | // | black height i + 1 | | black height i + 1 | | ||
| 1287 | // | | | | | ||
| 1288 | // ------------------------ ------------------------ | ||
| 1289 | */ | ||
| 1290 | 8704 | done = true; | |
| 1291 | 8704 | break; | |
| 1292 |
3/3✓ Branch 2 taken 28543 times.
✓ Branch 4 taken 3446 times.
✓ Branch 5 taken 25097 times.
|
28543 | } else if (this->getNodeColor(closeNephew) == Color::RED) { |
| 1293 | // The leaf-augmented subtree rooted at parent has this shape. | ||
| 1294 | // There is a black height violation at parent. | ||
| 1295 | /* | ||
| 1296 | // ??????????????????? | ||
| 1297 | // ? ? | ||
| 1298 | // ? K6 (parent) ? | ||
| 1299 | // ? ? | ||
| 1300 | // ??????????????????? | ||
| 1301 | // / \ | ||
| 1302 | // / \ | ||
| 1303 | // V V | ||
| 1304 | // BBBBBBBBBBBBBBBBB ---------------------- | ||
| 1305 | // B B | | | ||
| 1306 | // B K2 (sibling) B | black height i + 1 | | ||
| 1307 | // B B | | | ||
| 1308 | // BBBBBBBBBBBBBBBBB ---------------------- | ||
| 1309 | // / \ | ||
| 1310 | // / \ | ||
| 1311 | // V V | ||
| 1312 | // ------------------------ RRRRRRRRRRRRRRRRRRRR | ||
| 1313 | // | | R R | ||
| 1314 | // | black height i + 1 | R K4 (closeNephew) R | ||
| 1315 | // | | R R | ||
| 1316 | // ------------------------ RRRRRRRRRRRRRRRRRRRR | ||
| 1317 | // | | | ||
| 1318 | // | | | ||
| 1319 | // V V | ||
| 1320 | // ------------------------ | ||
| 1321 | // | | | ||
| 1322 | // | black height i + 1 | | ||
| 1323 | // | | | ||
| 1324 | // ------------------------ | ||
| 1325 | */ | ||
| 1326 |
1/1✓ Branch 2 taken 3446 times.
|
3446 | this->removeBlackLeafNodeHelper1(closeNephew, oppositeDirection, sibling, distantNephew); |
| 1327 | // The subtree has this shape: | ||
| 1328 | /* | ||
| 1329 | // ??????????????????? | ||
| 1330 | // ? ? | ||
| 1331 | // ? K6 (parent) ? | ||
| 1332 | // ? ? | ||
| 1333 | // ??????????????????? | ||
| 1334 | // / \ | ||
| 1335 | // / \ | ||
| 1336 | // V V | ||
| 1337 | // BBBBBBBBBBBBBBBBB ---------------------- | ||
| 1338 | // B B | | | ||
| 1339 | // B K4 (sibling) B | black height i + 1 | | ||
| 1340 | // B B | | | ||
| 1341 | // BBBBBBBBBBBBBBBBB ---------------------- | ||
| 1342 | // / \ | ||
| 1343 | // / \ | ||
| 1344 | // V V | ||
| 1345 | // RRRRRRRRRRRRRRRRRRRR ------------------------ | ||
| 1346 | // R R | | | ||
| 1347 | // R K2 (distantNephew) R | black height i + 1 | | ||
| 1348 | // R R | | | ||
| 1349 | // RRRRRRRRRRRRRRRRRRRR ------------------------ | ||
| 1350 | // | | | ||
| 1351 | // | | | ||
| 1352 | // V V | ||
| 1353 | // ------------------------ | ||
| 1354 | // | | | ||
| 1355 | // | black height i + 1 | | ||
| 1356 | // | | | ||
| 1357 | // ------------------------ | ||
| 1358 | */ | ||
| 1359 |
1/1✓ Branch 2 taken 3446 times.
|
3446 | this->removeBlackLeafNodeHelper2(parent, sibling, distantNephew, direction); |
| 1360 | // The subtree has this shape. The entire tree is a valid red-black tree. | ||
| 1361 | /* | ||
| 1362 | // BBBBBBBBBBBBBBBBB | ||
| 1363 | // B B | ||
| 1364 | // B K4 (sibling) B | ||
| 1365 | // B B | ||
| 1366 | // BBBBBBBBBBBBBBBBB | ||
| 1367 | // / \ | ||
| 1368 | // / \ | ||
| 1369 | // V V | ||
| 1370 | // BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBB | ||
| 1371 | // B B B B | ||
| 1372 | // B K2 (distantNephew) B B K6 (parent) B | ||
| 1373 | // B B B B | ||
| 1374 | // RRRRRRRRRRRRRRRRRRRR BBBBBBBBBBBBBBBBB | ||
| 1375 | // | | | | | ||
| 1376 | // | | | | | ||
| 1377 | // V V V V | ||
| 1378 | // ------------------------ ------------------------ | ||
| 1379 | // | | | | | ||
| 1380 | // | black height i + 1 | | black height i + 1 | | ||
| 1381 | // | | | | | ||
| 1382 | // ------------------------ ------------------------ | ||
| 1383 | */ | ||
| 1384 | 3446 | done = true; | |
| 1385 | 3446 | break; | |
| 1386 |
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|
25097 | } else if (this->getNodeColor(parent) == Color::RED) { |
| 1387 |
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|
9035 | this->m_nodes[sibling].m_color = Color::RED; |
| 1388 |
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|
9035 | this->m_nodes[parent].m_color = Color::BLACK; |
| 1389 | // The leaf-augmented tree rooted at parent has this shape. | ||
| 1390 | // The entire tree is a valid red-black tree. | ||
| 1391 | /* | ||
| 1392 | // BBBBBBBBBBBBBBBBBBB | ||
| 1393 | // B B | ||
| 1394 | // B K6 (parent) B | ||
| 1395 | // B B | ||
| 1396 | // BBBBBBBBBBBBBBBBBBB | ||
| 1397 | // / \ | ||
| 1398 | // / \ | ||
| 1399 | // V V | ||
| 1400 | // RRRRRRRRRRRRRRRRR ---------------------- | ||
| 1401 | // R R | | | ||
| 1402 | // R K2 (sibling) R | black height i + 1 | | ||
| 1403 | // R R | | | ||
| 1404 | // RRRRRRRRRRRRRRRRR ---------------------- | ||
| 1405 | // / \ | ||
| 1406 | // / \ | ||
| 1407 | // V V | ||
| 1408 | // BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB | ||
| 1409 | // B B B B | ||
| 1410 | // B K1 (distantNephew) B B K4 (closeNephew) B | ||
| 1411 | // B B B B | ||
| 1412 | // BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB | ||
| 1413 | // | | | | | ||
| 1414 | // | | | | | ||
| 1415 | // V V V V | ||
| 1416 | // ------------------------ ------------------------ | ||
| 1417 | // | | | | | ||
| 1418 | // | black height i | | black height i | | ||
| 1419 | // | | | | | ||
| 1420 | // ------------------------ ------------------------ | ||
| 1421 | */ | ||
| 1422 | 9035 | done = true; | |
| 1423 | 9035 | break; | |
| 1424 | } else { | ||
| 1425 | // The leaf-augmented subtree rooted at parent has this shape. | ||
| 1426 | /* | ||
| 1427 | // BBBBBBBBBBBBBBBBBBB | ||
| 1428 | // B B | ||
| 1429 | // B K6 (parent) B | ||
| 1430 | // B B | ||
| 1431 | // BBBBBBBBBBBBBBBBBBB | ||
| 1432 | // / \ | ||
| 1433 | // / \ | ||
| 1434 | // V V | ||
| 1435 | // BBBBBBBBBBBBBBBBB ---------------------- | ||
| 1436 | // B B | | | ||
| 1437 | // B K2 (sibling) B | black height i + 1 | | ||
| 1438 | // B B | | | ||
| 1439 | // BBBBBBBBBBBBBBBBB ---------------------- | ||
| 1440 | // / \ | ||
| 1441 | // / \ | ||
| 1442 | // V V | ||
| 1443 | // BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB | ||
| 1444 | // B B B B | ||
| 1445 | // B K1 (distantNephew) B B K4 (closeNephew) B | ||
| 1446 | // B B B B | ||
| 1447 | // BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB | ||
| 1448 | // | | | | | ||
| 1449 | // | | | | | ||
| 1450 | // V V V V | ||
| 1451 | // ------------------------ ------------------------ | ||
| 1452 | // | | | | | ||
| 1453 | // | black height i | | black height i | | ||
| 1454 | // | | | | | ||
| 1455 | // ------------------------ ------------------------ | ||
| 1456 | */ | ||
| 1457 |
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|
16062 | this->m_nodes[sibling].m_color = Color::RED; |
| 1458 | 16062 | node = parent; | |
| 1459 |
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|
16062 | parent = this->m_nodes[node].m_parent; |
| 1460 |
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16062 | if (parent == Node::NONE) { |
| 1461 | // The entire leaf-augmented tree has this shape. | ||
| 1462 | // The entire tree is a valid red-black tree. | ||
| 1463 | /* | ||
| 1464 | // BBBBBBBBBBBBBBBBBBB | ||
| 1465 | // B B | ||
| 1466 | // B K6 (node) B | ||
| 1467 | // B B | ||
| 1468 | // BBBBBBBBBBBBBBBBBBB | ||
| 1469 | // / \ | ||
| 1470 | // / \ | ||
| 1471 | // V V | ||
| 1472 | // RRRRRRRRRRRRRRRRR ---------------------- | ||
| 1473 | // R R | | | ||
| 1474 | // R K2 (sibling) R | black height i + 1 | | ||
| 1475 | // R R | | | ||
| 1476 | // RRRRRRRRRRRRRRRRR ---------------------- | ||
| 1477 | // / \ | ||
| 1478 | // / \ | ||
| 1479 | // V V | ||
| 1480 | // BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB | ||
| 1481 | // B B B B | ||
| 1482 | // B K1 (distantNephew) B B K4 (closeNephew) B | ||
| 1483 | // B B B B | ||
| 1484 | // BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB | ||
| 1485 | // | | | | | ||
| 1486 | // | | | | | ||
| 1487 | // V V V V | ||
| 1488 | // ------------------------ ------------------------ | ||
| 1489 | // | | | | | ||
| 1490 | // | black height i | | black height i | | ||
| 1491 | // | | | | | ||
| 1492 | // ------------------------ ------------------------ | ||
| 1493 | */ | ||
| 1494 | 1664 | done = true; | |
| 1495 | 1664 | break; | |
| 1496 | } else { | ||
| 1497 |
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|
14398 | direction = getDirectionFromParent(node); |
| 1498 | 14398 | oppositeDirection = Node::getOppositeDirection(direction); | |
| 1499 | // The leaf-augmented subtree rooted at parent has this | ||
| 1500 | // shape, assuming that direction == RIGHT: | ||
| 1501 | /* | ||
| 1502 | // ?????????????? | ||
| 1503 | // ? ? | ||
| 1504 | // ? parent ? | ||
| 1505 | // ? ? | ||
| 1506 | // ?????????????? | ||
| 1507 | // / \ | ||
| 1508 | // / \ | ||
| 1509 | // V V | ||
| 1510 | // ------------------------ BBBBBBBBBBBBBBBBBBB | ||
| 1511 | // | | B B | ||
| 1512 | // | black height i + 3 | B K6 (node) B | ||
| 1513 | // | | B B | ||
| 1514 | // ------------------------ BBBBBBBBBBBBBBBBBBB | ||
| 1515 | // / \ | ||
| 1516 | // / \ | ||
| 1517 | // V V | ||
| 1518 | // RRRRRRRRRRRRRRRRR ---------------------- | ||
| 1519 | // R R | | | ||
| 1520 | // R K2 (sibling) R | black height i + 1 | | ||
| 1521 | // R R | | | ||
| 1522 | // RRRRRRRRRRRRRRRRR ---------------------- | ||
| 1523 | // / \ | ||
| 1524 | // / \ | ||
| 1525 | // V V | ||
| 1526 | // BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB | ||
| 1527 | // B B B B | ||
| 1528 | // B K1 (distantNephew) B B K4 (closeNephew) B | ||
| 1529 | // B B B B | ||
| 1530 | // BBBBBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBBBBB | ||
| 1531 | // | | | | | ||
| 1532 | // | | | | | ||
| 1533 | // V V V V | ||
| 1534 | // ------------------------ ------------------------ | ||
| 1535 | // | | | | | ||
| 1536 | // | black height i | | black height i | | ||
| 1537 | // | | | | | ||
| 1538 | // ------------------------ ------------------------ | ||
| 1539 | // | ||
| 1540 | // There is a black height violation at parent because the | ||
| 1541 | // left subtree of parent has black height i + 3, and the | ||
| 1542 | // right subtree has black height i + 2. So we need at | ||
| 1543 | // least one more loop iteration. After incrementing i, the | ||
| 1544 | // invariant at the top of the loop is satisfied. | ||
| 1545 | */ | ||
| 1546 | } | ||
| 1547 | } | ||
| 1548 | } | ||
| 1549 | 34335 | FW_ASSERT(done); | |
| 1550 | // The tree is a valid red-black tree. | ||
| 1551 | 34335 | } | |
| 1552 | |||
| 1553 | //! This is a helper function for removeBlackLeafNode. sibling and | ||
| 1554 | //! distantNephew are in-out parameters (they are both read and written). | ||
| 1555 | 5752 | void removeBlackLeafNodeHelper1(Index closeNephew, //!< The close nephew (input) | |
| 1556 | Direction oppositeDirection, //!< The opposite direction (input) | ||
| 1557 | Index& sibling, //!< The sibling (input and output) | ||
| 1558 | Index& distantNephew //!< The distant nephew (input and output) | ||
| 1559 | ) { | ||
| 1560 | 5752 | FW_ASSERT(sibling != Node::NONE); | |
| 1561 | 5752 | FW_ASSERT(closeNephew != Node::NONE); | |
| 1562 | 5752 | this->rotateSubtree(sibling, oppositeDirection); | |
| 1563 | 5752 | this->m_nodes[sibling].m_color = Color::RED; | |
| 1564 | 5752 | this->m_nodes[closeNephew].m_color = Color::BLACK; | |
| 1565 | 5752 | distantNephew = sibling; | |
| 1566 | 5752 | sibling = closeNephew; | |
| 1567 | 5752 | } | |
| 1568 | |||
| 1569 | //! This is a helper function for removeBlackLeafNode. | ||
| 1570 | 19808 | void removeBlackLeafNodeHelper2(Index parent, //!< The parent | |
| 1571 | Index sibling, //!< The sibling | ||
| 1572 | Index distantNephew, //!< The distant nephew | ||
| 1573 | Direction direction //!< The direction | ||
| 1574 | ) { | ||
| 1575 | 19808 | this->rotateSubtree(parent, direction); | |
| 1576 | 19808 | this->m_nodes[sibling].m_color = this->m_nodes[parent].m_color; | |
| 1577 | 19808 | this->m_nodes[parent].m_color = Color::BLACK; | |
| 1578 | 19808 | this->m_nodes[distantNephew].m_color = Color::BLACK; | |
| 1579 | 19808 | } | |
| 1580 | |||
| 1581 | //! This function removes a node of the tree. On entry, node stores the key | ||
| 1582 | //! and value to be removed. It must not be NONE. On return, removedNode | ||
| 1583 | //! stores the node that was actually removed. | ||
| 1584 | 62668 | void removeNode(Index node, //!< The node to remove (input) | |
| 1585 | Index& removedNode //!< The node actually removed (output) | ||
| 1586 | ) { | ||
| 1587 |
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|
62668 | if ((this->m_nodes[node].m_left) != Node::NONE && (this->m_nodes[node].m_right != Node::NONE)) { |
| 1588 | 344 | this->removeNodeWithTwoChildren(node, removedNode); | |
| 1589 | } else { | ||
| 1590 | 62324 | this->removeNodeWithAtMostOneChild(node); | |
| 1591 | 62324 | removedNode = node; | |
| 1592 | } | ||
| 1593 | 62668 | } | |
| 1594 | |||
| 1595 | //! This function removes a node of the tree with at most one child. On | ||
| 1596 | //! entry, node stores the node to be removed. It must not be NONE. | ||
| 1597 | 62668 | void removeNodeWithAtMostOneChild(Index node //!< The node to remove | |
| 1598 | ) { | ||
| 1599 | 62668 | FW_ASSERT(node != Node::NONE); | |
| 1600 |
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62668 | if (this->m_nodes[node].m_left != Node::NONE) { |
| 1601 | 340 | this->removeNodeWithOneChild(node, Direction::LEFT); | |
| 1602 |
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62328 | } else if (this->m_nodes[node].m_right != Node::NONE) { |
| 1603 | 26118 | this->removeNodeWithOneChild(node, Direction::RIGHT); | |
| 1604 |
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36210 | } else if (node == this->m_root) { |
| 1605 | 871 | this->m_root = Node::NONE; | |
| 1606 |
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35339 | } else if (this->m_nodes[node].m_color == Color::RED) { |
| 1607 | 1004 | this->removeRedLeafNode(node); | |
| 1608 | } else { | ||
| 1609 | 34335 | this->removeBlackLeafNode(node); | |
| 1610 | } | ||
| 1611 | 62668 | } | |
| 1612 | |||
| 1613 | //! This function removes a node of the tree with exactly one child. node | ||
| 1614 | //! stores the node to remove. It must not be NONE. direction stores the | ||
| 1615 | //! direction of the child. | ||
| 1616 | 26458 | void removeNodeWithOneChild(Index node, //!< The node | |
| 1617 | Direction direction //!< The direction of the child | ||
| 1618 | ) { | ||
| 1619 | // Since the tree is a valid red-black tree, a node with exactly one | ||
| 1620 | // child must be black, and the child must be red. | ||
| 1621 | 26458 | FW_ASSERT(this->m_nodes[node].m_color == Color::BLACK, | |
| 1622 | static_cast<FwAssertArgType>(this->m_nodes[node].m_color)); | ||
| 1623 | 26458 | const auto parent = this->m_nodes[node].m_parent; | |
| 1624 | 26458 | const auto child = this->m_nodes[node].getChild(direction); | |
| 1625 | 26458 | FW_ASSERT(this->m_nodes[child].m_color == Color::RED, | |
| 1626 | static_cast<FwAssertArgType>(this->m_nodes[node].m_color)); | ||
| 1627 |
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26458 | if (parent == Node::NONE) { |
| 1628 | 697 | this->m_root = child; | |
| 1629 | } else { | ||
| 1630 | 25761 | const auto parentDirection = this->getDirectionFromParent(node); | |
| 1631 | 25761 | this->m_nodes[parent].setChild(parentDirection, child); | |
| 1632 | } | ||
| 1633 | 26458 | this->m_nodes[child].m_parent = parent; | |
| 1634 | 26458 | this->m_nodes[child].m_color = Color::BLACK; | |
| 1635 | 26458 | } | |
| 1636 | |||
| 1637 | //! This function removes a node of the tree that has two children. On | ||
| 1638 | //! entry, node stores the key and value to be removed. It must not be NONE, | ||
| 1639 | //! and it must have two children. On return, removedNode stores the node | ||
| 1640 | //! that was actually removed. | ||
| 1641 | 344 | void removeNodeWithTwoChildren(Index node, //!< The node to remove (input) | |
| 1642 | Index& removedNode //!< The node actually removed (output) | ||
| 1643 | ) { | ||
| 1644 | 344 | const auto rightChild = this->m_nodes[node].m_right; | |
| 1645 | 344 | removedNode = this->getOuterNodeUnder(rightChild, Direction::LEFT); | |
| 1646 | 344 | this->m_nodes[node].m_entry = this->m_nodes[removedNode].m_entry; | |
| 1647 | 344 | this->removeNodeWithAtMostOneChild(removedNode); | |
| 1648 | 344 | } | |
| 1649 | |||
| 1650 | //! This function removes a node that is colored red and is a leaf node | ||
| 1651 | //! (i.e., it has no children) and is not the root. node stores the node to | ||
| 1652 | //! remove. It must not be NONE. | ||
| 1653 | 1004 | void removeRedLeafNode(Index node //!< The node to remove | |
| 1654 | ) { | ||
| 1655 | 1004 | FW_ASSERT(node != this->m_root); | |
| 1656 | 1004 | const auto& nodeObj = this->m_nodes[node]; | |
| 1657 | 1004 | FW_ASSERT(nodeObj.m_color == Color::RED); | |
| 1658 | 1004 | FW_ASSERT(nodeObj.m_left == Node::NONE); | |
| 1659 | 1004 | FW_ASSERT(nodeObj.m_right == Node::NONE); | |
| 1660 | 1004 | const auto parent = nodeObj.m_parent; | |
| 1661 | 1004 | const auto direction = this->getDirectionFromParent(node); | |
| 1662 | 1004 | this->m_nodes[parent].setChild(direction, Node::NONE); | |
| 1663 | 1004 | } | |
| 1664 | |||
| 1665 | //! This function performs a left or right rotation on the subtree whose | ||
| 1666 | //! root is node. The following invariants must hold on entry to this | ||
| 1667 | //! function, or an assertion failure will occur: | ||
| 1668 | //! | ||
| 1669 | //! 1. node must not be NONE. | ||
| 1670 | //! | ||
| 1671 | //! 2. The child of node in the direction opposite direction must not be | ||
| 1672 | //! NONE. | ||
| 1673 | 86132 | void rotateSubtree(Index node, //!< The node index | |
| 1674 | Direction direction //!< The direction | ||
| 1675 | ) { | ||
| 1676 | // We assume that the tree is a binary search tree (BST). | ||
| 1677 | 86132 | FW_ASSERT(node != Node::NONE); | |
| 1678 | 86132 | const auto parent = this->m_nodes[node].m_parent; | |
| 1679 | 86132 | const auto oppositeDirection = Node::getOppositeDirection(direction); | |
| 1680 | 86132 | const auto newRoot = this->m_nodes[node].getChild(oppositeDirection); | |
| 1681 | 86132 | FW_ASSERT(newRoot != Node::NONE); | |
| 1682 | 86132 | const auto newChild = this->m_nodes[newRoot].getChild(direction); | |
| 1683 | 86132 | this->m_nodes[node].setChild(oppositeDirection, newChild); | |
| 1684 |
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86132 | if (newChild != Node::NONE) { |
| 1685 | 39761 | this->m_nodes[newChild].m_parent = node; | |
| 1686 | } | ||
| 1687 | 86132 | this->m_nodes[newRoot].setChild(direction, node); | |
| 1688 | 86132 | this->m_nodes[newRoot].m_parent = parent; | |
| 1689 |
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86132 | if (parent != Node::NONE) { |
| 1690 | 81785 | const auto parentDirection = getDirectionFromParent(node); | |
| 1691 | 81785 | this->m_nodes[parent].setChild(parentDirection, newRoot); | |
| 1692 | } else { | ||
| 1693 | 4347 | this->m_root = newRoot; | |
| 1694 | } | ||
| 1695 | 86132 | this->m_nodes[node].m_parent = newRoot; | |
| 1696 | // The tree is a BST. | ||
| 1697 | 86132 | } | |
| 1698 | |||
| 1699 | private: | ||
| 1700 | // ---------------------------------------------------------------------- | ||
| 1701 | // Private member variables | ||
| 1702 | // ---------------------------------------------------------------------- | ||
| 1703 | |||
| 1704 | //! The array for storing the tree nodes | ||
| 1705 | Nodes m_nodes = {}; | ||
| 1706 | |||
| 1707 | //! The stack of indices of free nodes. The indices point into m_nodes. | ||
| 1708 | FreeNodes m_freeNodes = {}; | ||
| 1709 | |||
| 1710 | //! The index of the root node | ||
| 1711 | Index m_root = Node::NONE; | ||
| 1712 | }; | ||
| 1713 | |||
| 1714 | } // namespace Fw | ||
| 1715 | |||
| 1716 | #endif | ||
| 1717 |